# Table 1: Financial Mathematics and Statistics

Unit of study |
Credit points |
A: Assumed knowledge P: Prerequisites C: Corequisites N: Prohibition |
Session |
---|---|---|---|

## Financial Mathematics and Statistics |
|||

For a major in Financial Mathematics and Statistics, students are required to complete: | |||

(i) MATH3075/3975; | |||

(ii) STAT3021/3921 | |||

(iii) STAT3022/3922; and | |||

(iv) One of the following units of study: MATH3076/3976, MATH3078/3978, MATH3969, MATH3974, STAT3888, FMAT3888, DATA3404, MATH3971, STAT3914 or STAT3023/3923 | |||

## Junior units of study |
|||

MATH1021Calculus Of One Variable |
3 | A HSC Mathematics Extension 1 or equivalent. N MATH1011 or MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 |
Intensive January Semester 1 Semester 2 |

MATH1921Calculus Of One Variable (Advanced) |
3 | A (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. N MATH1001 or MATH1011 or MATH1906 or ENVX1001 or MATH1901 or MATH1021 or MATH1931 Note: Department permission required for enrolment |
Semester 1 |

MATH1931Calculus Of One Variable (SSP) |
3 | A (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. N MATH1001 or MATH1011 or MATH1901 or ENVX1001 or MATH1906 or MATH1021 or MATH1921 Note: Department permission required for enrolmentEnrolment is by invitation only |
Semester 1 |

MATH1002Linear Algebra |
3 | A HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). N MATH1012 or MATH1014 or MATH1902 |
Intensive January Semester 1 |

MATH1902Linear Algebra (Advanced) |
3 | A (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent N MATH1002 or MATH1014 Note: Department permission required for enrolment |
Semester 1 |

MATH1004Discrete Mathematics |
3 | A HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). N MATH1904 or MATH1064 |
Semester 2 |

MATH1904Discrete Mathematics (Advanced) |
3 | A Strong skills in mathematical problem solving and theory, including coordinate geometry, integral and differential calculus, and solution of polynomial equations equivalent to HSC Mathematics Extension 2 or a Band E4 in HSC Mathematics Extension 1 N MATH1004 or MATH1064 Note: Department permission required for enrolment |
Semester 2 |

MATH1023Multivariable Calculus and Modelling |
3 | A Knowledge of complex numbers and methods of differential and integral calculus including integration by partial fractions and integration by parts as for example in MATH1021 or MATH1921 or MATH1931 or HSC Mathematics Extension 2 N MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 |
Intensive January Semester 1 Semester 2 |

MATH1923Multivariable Calculus and Modelling (Adv) |
3 | A (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. N MATH1003 or MATH1013 or MATH1907 or MATH1903 or MATH1023 or MATH1933 Note: Department permission required for enrolment |
Semester 2 |

MATH1933Multivariable Calculus and Modelling (SSP) |
3 | A (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. N MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923 Note: Department permission required for enrolmentEnrolment is by invitation only. |
Semester 2 |

MATH1005Statistical Thinking with Data |
3 | A HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). N MATH1015 or MATH1905 or STAT1021 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or DATA1901 |
Intensive January Semester 1 Semester 2 |

MATH1905Statistical Thinking with Data (Advanced) |
3 | A (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent N MATH1005 or MATH1015 or STAT1021 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or DATA1901 Note: Department permission required for enrolment |
Semester 2 |

MATH1001Differential Calculus This unit of study is not available in 2020 |
3 | A HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). C MATH1003 or MATH1903 N MATH1011 or MATH1901 or MATH1906 or MATH1111 or ENVX1001. |
Semester 1 Summer Main |

MATH1003Integral Calculus and Modelling This unit of study is not available in 2020 |
3 | A HSC Mathematics Extension 1 or MATH1001 or MATH1011 or a credit or higher in MATH1111. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). N MATH1013 or MATH1903 or MATH1907 |
Summer Main |

DATA1001Foundations of Data Science |
6 | N DATA1901 or MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 |
Semester 1 Semester 2 |

DATA1901Foundations of Data Science (Adv) |
6 | A An ATAR of 95 or more N MATH1905 or ECMT1010 or ENVX1002 or BUSS1020 or DATA1001 or MATH1115 or MATH1015 |
Semester 1 Semester 2 |

## Intermediate units of study |
|||

DATA2002Data Analytics: Learning from Data |
6 | A Basic linear algebra and some coding for example MATH1014 or MATH1002 or MATH1902 and DATA1001 or DATA1901 P [DATA1001 or ENVX1001 or ENVX1002] or [MATH10X5 and MATH1115] or [MATH10X5 and STAT2X11] or [MATH1905 and MATH1XXX (except MATH1XX5)] or [BUSS1020 or ECMT1010 or STAT1021] N STAT2012 or STAT2912 or DATA2902 |
Semester 2 |

DATA2902Data Analytics: Learning from Data (Adv) |
6 | A Basic linear algebra and some coding for example MATH1014 or MATH1002 or MATH1902 and DATA1001 or DATA1901 P A mark of 65 or above in any of the following (DATA1001 or DATA1901 or ENVX1001 or ENVX1002) or (MATH10X5 and MATH1115) or (MATH10X5 and STAT2011) or STAT2911 or (MATH1905 and MATH1XXX [except MATH1XX5]) or (BUSS1020 or ECMT1010 or STAT1021) N STAT2012 or STAT2912 or DATA2002 |
Semester 2 |

MATH2070Optimisation and Financial Mathematics |
6 | A MATH1X23 or MATH1933 or MATH1X03 or MATH1907 P (MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02) N MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510 Students may enrol in both MATH2070 and MATH3075 in the same semester |
Semester 2 |

MATH2970Optimisation and Financial Mathematics Adv |
6 | A MATH19X3 or MATH1907 or a mark of 65 or above in MATH1003 or MATH1023 P [MATH19X1 or MATH1906 or (a mark of 65 or above in MATH1021 or MATH1001)] and [MATH1902 or (a mark of 65 or above in MATH1002)] N MATH2010 or MATH2033 or MATH2933 or MATH2070 or ECMT3510 Students may enrol in both MATH2970 and MATH3975 in the same semester |
Semester 2 |

STAT2011Probability and Estimation Theory |
6 | P (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) N STAT2911 |
Semester 1 |

STAT2911Probability and Statistical Models (Adv) |
6 | P (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and a mark of 65 or greater in (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) N STAT2011 |
Semester 1 |

## Senior core units of study |
|||

MATH3075Financial Derivatives |
6 | P 12 credit points chosen from MATH2XXX or STAT2XXX or DATA2X02 N MATH3975 or MATH3015 or MATH3933 It is possible to enrol in MATH2070 and MATH3075 in the same semester |
Semester 2 |

MATH3975Financial Derivatives (Advanced) |
6 | P A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02) N MATH3933 or MATH3015 or MATH3075 MATH2X70 and MATH3975 may be taken in the same semester |
Semester 2 |

STAT3021Stochastic Processes |
6 | P STAT2X11 and (MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933) N STAT3911 or STAT3011 |
Semester 1 |

STAT3921Stochastic Processes (Advanced) |
6 | P (STAT2011 or STAT2911) and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 N STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT4021 |
Semester 1 |

STAT3022Applied Linear Models |
6 | P STAT2X11 and (DATA2X02 or STAT2X12) N STAT3912 or STAT3012 or STAT3922 |
Semester 1 |

STAT3922Applied Linear Models (Advanced) |
6 | P STAT2X11 and [a mark of 65 or greater in (STAT2X12 or DATA2X02)] N STAT3912 or STAT3012 or STAT3022 |
Semester 1 |

## Senior elective units of study |
|||

STAT3023Statistical Inference |
6 | A DATA2X02 or STAT2X12 P STAT2X11 N STAT3913 or STAT3013 or STAT3923 |
Semester 2 |

STAT3923Statistical Inference (Advanced) |
6 | P STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12) N STAT3913 or STAT3013 or STAT3023 |
Semester 2 |

STAT3888Statistical Machine Learning |
6 | A STAT3012 or STAT3912 or STAT3022 or STAT3922 P STAT2X11 and (DATA2X02 or STAT2X12) N STAT3914 or STAT3014 |
Semester 2 |

STAT3914Applied Statistics Advanced This unit of study is not available in 2020 |
6 | A STAT3012 or STAT3912 or STAT3022 or STAT3922 P STAT2912 or (a mark of 65 or above in STAT2012 or DATA2002) N STAT3014 or STAT3907 or STAT3902 or STAT3006 or STAT3002 |
Semester 2 |

FMAT3888Projects in Financial Mathematics |
6 | A STAT2X11, MATH2X70 P (MATH2070 or MATH2970) and (STAT2011 or STAT2911) |
Semester 2 |

MATH3971Convex Analysis and Optimal Control (Adv) |
6 | A MATH2X21 and MATH2X23 and STAT2X11 P A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02) N MATH4071 |
Semester 1 |

MATH3076Mathematical Computing |
6 | P 12cp of MATH2XXX or [6cp of MATH2XXX and (6cp of STAT2XXX or DATA2X02)] N MATH3976 or MATH4076 |
Semester 1 |

MATH3976Mathematical Computing (Advanced) |
6 | A Strong skills in linear algebra and the theory and methods of ordinary and partial differential equations for example (MATH2961 and MATH2965) or (MATH2921 and MATH2922) P A mark of 65 or above in [(12cp of MATH2XXX) or (6cp of MATH2XXX and 6cp of STAT2XXX or DATA2X02)] N MATH3076 or MATH4076 |
Semester 1 |

MATH3078PDEs and Waves |
6 | A [MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22] P 12 credit points of MATH2XXX units of study N MATH3978 or MATH4078 |
Semester 2 |

MATH3978PDEs and Waves (Advanced) |
6 | A [MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22] P A mark of 65 or greater in 12 credit points of MATH2XXX units of study N MATH3078 or MATH4078 |
Semester 2 |

MATH3969Measure Theory and Fourier Analysis (Adv) |
6 | A Real analysis and vector spaces. For example MATH2X21 and MATH2X23 P A mark of 65 or greater in 12 credit points of MATH2XXX units of study N MATH4069 |
Semester 2 |

MATH3974Fluid Dynamics (Advanced) |
6 | A [MATH2961 and MATH2965] or [MATH2921 and MATH2922] P Credit average or greater in 12 credit points of Intermediate Mathematics N MATH4074 |
Semester 1 |

DATA3404Data Science Platforms |
6 | A This unit of study assumes that students have previous knowledge of database structures and of SQL. The prerequisite material is covered in DATA2001 or ISYS2120. Familiarity with a programming language (e.g. Java or C) is also expected. P DATA2001 OR DATA2901 OR ISYS2120 OR INFO2120 OR INFO2820 N INFO3504 OR INFO3404 |
Semester 1 |

### Financial Mathematics and Statistics

For a major in Financial Mathematics and Statistics, students are required to complete:

(i) MATH3075/3975;

(ii) STAT3021/3921

(iii) STAT3022/3922; and

(iv) One of the following units of study: MATH3076/3976, MATH3078/3978, MATH3969, MATH3974, STAT3888, FMAT3888, DATA3404, MATH3971, STAT3914 or STAT3023/3923

##### Junior units of study

**MATH1021 Calculus Of One Variable**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Intensive January,Semester 1,Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1011 or MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 Assumed knowledge: HSC Mathematics Extension 1 or equivalent. Assessment: 2 x quizzes (30%), 2 x assignments (5%), online quizzes (10%), final exam (55%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals.

Textbooks

Calculus of One Variable (Course Notes for MATH1021)

**MATH1921 Calculus Of One Variable (Advanced)**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1001 or MATH1011 or MATH1906 or ENVX1001 or MATH1901 or MATH1021 or MATH1931 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: 2 x quizzes (20%); 2 x assignments (10%); final exam (70%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals. Additional theoretical topics included in this advanced unit include the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1931 Calculus Of One Variable (SSP)**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1 Classes: 2x1-hr lectures; and 1x1-hr tutorial/wk Prohibitions: MATH1001 or MATH1011 or MATH1901 or ENVX1001 or MATH1906 or MATH1021 or MATH1921 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: Seminar participation (10%); 3 x special assignments (10%); 2 x quizzes (16%); 2 x assignments (8%); final exam (56%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Note: Enrolment is by invitation only

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1921 Calculus of One Variable (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

**MATH1002 Linear Algebra**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Intensive January,Semester 1 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1012 or MATH1014 or MATH1902 Assumed knowledge: HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: online quizzes (10%), quiz (15%), assignments (10%), final exam (65%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1002 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.

This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.

This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.

Textbooks

Linear Algebra: A Modern Introduction, (4th edition), David Poole

**MATH1902 Linear Algebra (Advanced)**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1002 or MATH1014 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: Online quizzes (10%); 4 x assignments (20%); final exam (70%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. It parallels the normal unit MATH1002 but goes more deeply into the subject matter and requires more mathematical sophistication.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1004 Discrete Mathematics**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1904 or MATH1064 Assumed knowledge: HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: 2 x quizzes (30%); 2 x assignments (5%); final exam (65%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to fundamental aspects of discrete mathematics, which deals with 'things that come in chunks that can be counted'. It focuses on the enumeration of a set of numbers, viz. Catalan numbers. Topics include sets and functions, counting principles, discrete probability, Boolean expressions, mathematical induction, linear recurrence relations, graphs and trees.

Textbooks

Introduction to Discrete Mathematics, K G Choo and D E Taylor, Addison Wesley Long-man Australia, (1998)

**MATH1904 Discrete Mathematics (Advanced)**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1004 or MATH1064 Assumed knowledge: Strong skills in mathematical problem solving and theory, including coordinate geometry, integral and differential calculus, and solution of polynomial equations equivalent to HSC Mathematics Extension 2 or a Band E4 in HSC Mathematics Extension 1 Assessment: 2 x quizzes (30%); 2 x assignments (5%); final exam (65%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

This unit is designed to provide a thorough preparation for further study in mathematics. It parallels the normal unit MATH1004 but goes more deeply into the subject matter and requires more mathematical sophistication.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1023 Multivariable Calculus and Modelling**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Intensive January,Semester 1,Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 Assumed knowledge: Knowledge of complex numbers and methods of differential and integral calculus including integration by partial fractions and integration by parts as for example in MATH1021 or MATH1921 or MATH1931 or HSC Mathematics Extension 2 Assessment: 2 x quizzes (30%), 2 x assignments (5%), online quizzes (10%), final exam (55%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable.

Textbooks

Multivariable Calculus and Modelling (Course Notes for MATH1023)

**MATH1923 Multivariable Calculus and Modelling (Adv)**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 2 Classes: 2x1-hr lectures; and 1x1-hr tutorial/wk Prohibitions: MATH1003 or MATH1013 or MATH1907 or MATH1903 or MATH1023 or MATH1933 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: 2 x quizzes (20%); 2 x assignments (10%); final exam (70%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable. Additional topics covered in this advanced unit of study include the use of diagonalisation of matrices to study systems of linear equation and optimisation problems, limits of functions of two or more variables, and the derivative of a function of two or more variables.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1933 Multivariable Calculus and Modelling (SSP)**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 2 Classes: 2x1-hr lectures; and 1x1-hr tutorial/wk Prohibitions: MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: Seminar participation (10%); 3 x special assignments (10%); 2 x quizzes (16%); 2 x assignments (8%); final exam (56%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Note: Enrolment is by invitation only.

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1923 Multivariable Calculus and Modelling (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

**MATH1005 Statistical Thinking with Data**

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Intensive January,Semester 1,Semester 2 Classes: 2x1-hr lectures; 1x1-hr lab/wk Prohibitions: MATH1015 or MATH1905 or STAT1021 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or DATA1901 Assumed knowledge: HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: quizzes (10%), project 1 (10%), project 2 (15%), final exam (65%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

In a data-rich world, global citizens need to problem solve with data, and evidence based decision-making is essential is every field of research and work.

This unit equips you with the foundational statistical thinking to become a critical consumer of data. You will learn to think analytically about data and to evaluate the validity and accuracy of any conclusions drawn. Focusing on statistical literacy, the unit covers foundational statistical concepts, including the design of experiments, exploratory data analysis, sampling and tests of significance.

This unit equips you with the foundational statistical thinking to become a critical consumer of data. You will learn to think analytically about data and to evaluate the validity and accuracy of any conclusions drawn. Focusing on statistical literacy, the unit covers foundational statistical concepts, including the design of experiments, exploratory data analysis, sampling and tests of significance.

Textbooks

Statistics, (4th Edition), Freedman Pisani Purves (2007)

**MATH1905 Statistical Thinking with Data (Advanced)**

Credit points: 3 Teacher/Coordinator: Prof Qiying Wang Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1005 or MATH1015 or STAT1021 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or DATA1901 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: 2 x quizzes (20%); 2 x assignments (10%); final exam (70%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. This Advanced level unit of study parallels the normal unit MATH1005 but goes more deeply into the subject matter and requires more mathematical sophistication.

Textbooks

A Primer of Statistics (4th edition), M C Phipps and M P Quine, Prentice Hall, Australia (2001)

**MATH1001 Differential Calculus**

*This unit of study is not available in 2020*

Credit points: 3 Session: Semester 1,Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Corequisites: MATH1003 or MATH1903 Prohibitions: MATH1011 or MATH1901 or MATH1906 or MATH1111 or ENVX1001. Assumed knowledge: HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1001 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. This unit of study looks at complex numbers, functions of a single variable, limits and continuity, vector functions and functions of two variables. Differential calculus is extended to functions of two variables. Taylor's theorem as a higher order mean value theorem.

Textbooks

As set out in the Junior Mathematics Handbook.

**MATH1003 Integral Calculus and Modelling**

*This unit of study is not available in 2020*

Credit points: 3 Session: Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1013 or MATH1903 or MATH1907 Assumed knowledge: HSC Mathematics Extension 1 or MATH1001 or MATH1011 or a credit or higher in MATH1111. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1003 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.This unit of study first develops the idea of the definite integral from Riemann sums, leading to the Fundamental Theorem of Calculus. Various techniques of integration are considered, such as integration by parts.The second part is an introduction to the use of first and second order differential equations to model a variety of scientific phenomena.

Textbooks

As set out in the Junior Mathematics Handbook

**DATA1001 Foundations of Data Science**

Credit points: 6 Teacher/Coordinator: Prof Qiying Wang Session: Semester 1,Semester 2 Classes: 3x1-hr lectures; 1x2-hr lab/wk Prohibitions: DATA1901 or MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 Assessment: RQuizzes (10%); 3 x projects (30%); final exam (60%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

DATA1001 is a foundational unit in the Data Science major. The unit focuses on developing critical and statistical thinking skills for all students. Does mobile phone usage increase the incidence of brain tumours? What is the public's attitude to shark baiting following a fatal attack? Statistics is the science of decision making, essential in every industry and undergirds all research which relies on data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem solving skills in a team setting. Taught interactively with embedded technology, DATA1001 develops critical thinking and skills to problem-solve with data. It is the prerequisite for DATA2002.

Textbooks

Statistics, (4th Edition), Freedman Pisani Purves (2007)

**DATA1901 Foundations of Data Science (Adv)**

Credit points: 6 Teacher/Coordinator: Prof Qiying Wang Session: Semester 1,Semester 2 Classes: Lecture 3 hrs/week + Computer lab 2 hr/week Prohibitions: MATH1905 or ECMT1010 or ENVX1002 or BUSS1020 or DATA1001 or MATH1115 or MATH1015 Assumed knowledge: An ATAR of 95 or more Assessment: RQuizzes (10%), Projects (30%), Final Exam (60%). Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

DATA1901 is an advanced level unit (matching DATA1001) that is foundational to the new major in Data Science. The unit focuses on developing critical and statistical thinking skills for all students. Does mobile phone usage increase the incidence of brain tumours? What is the public's attitude to shark baiting following a fatal attack? Statistics is the science of decision making, essential in every industry and undergirds all research which relies on data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem solving skills in a team setting. Taught interactively with embedded technology and masterclasses, DATA1901 develops critical thinking and skills to problem-solve with data at an advanced level. By completing this unit you will have an excellent foundation for pursuing data science, whether directly through the data science major, or indirectly in whatever field you major in. The advanced unit has the same overall concepts as the regular unit but material is discussed in a manner that offers a greater level of challenge and academic rigour.

Textbooks

All learning materials will be on Canvas. In addition, the textbook is Statistics (4th Edition) { Freedman, Pisani, and Purves (2007), which is available in 3 forms: 1) E-text $65 (www.wileydirect.com.au/buy/statistics-4th-international-student-edition/), 2) hard copy (Co-op Bookshop), and 3) the Library.

##### Intermediate units of study

**DATA2002 Data Analytics: Learning from Data**

Credit points: 6 Teacher/Coordinator: A/Prof Jennifer Chan Session: Semester 2 Classes: Lecture 3 hrs/week + workshop 2 hr/week Prerequisites: [DATA1001 or ENVX1001 or ENVX1002] or [MATH10X5 and MATH1115] or [MATH10X5 and STAT2X11] or [MATH1905 and MATH1XXX (except MATH1XX5)] or [BUSS1020 or ECMT1010 or STAT1021] Prohibitions: STAT2012 or STAT2912 or DATA2902 Assumed knowledge: Basic linear algebra and some coding for example MATH1014 or MATH1002 or MATH1902 and DATA1001 or DATA1901 Assessment: Model reports (15%), online quizzes (15%), group work assignment and presentation (20%) and final exam (50%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Technological advances in science, business and engineering have given rise to a proliferation of data from all aspects of our life. Understanding the information presented in these data is critical as it enables informed decision making into many areas including market intelligence and science. DATA2002 is an intermediate unit in statistics and data sciences, focusing on learning data analytic skills for a wide range of problems and data. How should the Australian government measure and report employment and unemployment? Can we tell the difference between decaffeinated and regular coffee ? In this unit, you will learn how to ingest, combine and summarise data from a variety of data models which are typically encountered in data science projects as well as reinforcing your programming skills through experience with a statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skill to analyse various types of data in order to answer a scientific question. From this unit, you will develop knowledge and skills that will enable you to embrace data analytic challenges stemming from everyday problems.

**DATA2902 Data Analytics: Learning from Data (Adv)**

Credit points: 6 Teacher/Coordinator: A/Prof Jennifer Chan Session: Semester 2 Classes: Lecture 3 hrs/week + workshop 2 hr/week Prerequisites: A mark of 65 or above in any of the following (DATA1001 or DATA1901 or ENVX1001 or ENVX1002) or (MATH10X5 and MATH1115) or (MATH10X5 and STAT2011) or STAT2911 or (MATH1905 and MATH1XXX [except MATH1XX5]) or (BUSS1020 or ECMT1010 or STAT1021) Prohibitions: STAT2012 or STAT2912 or DATA2002 Assumed knowledge: Basic linear algebra and some coding for example MATH1014 or MATH1002 or MATH1902 and DATA1001 or DATA1901 Assessment: Model reports (15%), online quizzes (15%), group work assignment and presentation (20%) and final exam (50%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Technological advances in science, business, and engineering have given rise to a proliferation of data from all aspects of our life. Understanding the information presented in these data is critical as it enables informed decision making into many areas including market intelligence and science. DATA2902 is an intermediate unit in statistics and data sciences, focusing on learning advanced data analytic skills for a wide range of problems and data. How should the Australian government measure and report employment and unemployment? Can we tell the difference between decaffeinated and regular coffee? In this unit, you will learn how to ingest, combine and summarise data from a variety of data models which are typically encountered in data science projects as well as reinforcing your programming skills through experience with statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skill to analyse various types of data in order to answer a scientific question. From this unit, you will develop knowledge and skills that will enable you to embrace data analytic challenges stemming from everyday problems.

**MATH2070 Optimisation and Financial Mathematics**

Credit points: 6 Teacher/Coordinator: Prof Martin Wechslberger Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk Prerequisites: (MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02) Prohibitions: MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510 Assumed knowledge: MATH1X23 or MATH1933 or MATH1X03 or MATH1907 Assessment: 1 x2 exam (70%) , 1 x assignments (10%), 1 x quizzes (10%); 1 x computational project (10%). To pass the course at least 50% in the final exam is necessary. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Students may enrol in both MATH2070 and MATH3075 in the same semester

Problems in industry and commerce often involve maximising profits or minimising costs subject to constraints arising from resource limitations. The first part of this unit looks at programming problems and their solution using the simplex algorithm; nonlinear optimisation and the Kuhn Tucker conditions.

The second part of the unit deals with utility theory and modern portfolio theory. Topics covered include: pricing under the principles of expected return and expected utility; mean-variance Markowitz portfolio theory, the Capital Asset Pricing Model, log-optimal portfolios and the Kelly criterion; dynamical programming. Some understanding of probability theory including distributions and expectations is required in this part.

Theory developed in lectures will be complemented by computer laboratory sessions using MATLAB. Minimal computing experience will be required.

The second part of the unit deals with utility theory and modern portfolio theory. Topics covered include: pricing under the principles of expected return and expected utility; mean-variance Markowitz portfolio theory, the Capital Asset Pricing Model, log-optimal portfolios and the Kelly criterion; dynamical programming. Some understanding of probability theory including distributions and expectations is required in this part.

Theory developed in lectures will be complemented by computer laboratory sessions using MATLAB. Minimal computing experience will be required.

**MATH2970 Optimisation and Financial Mathematics Adv**

Credit points: 6 Teacher/Coordinator: Prof Martin Wechslberger Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk (lectures given in common with MATH2070). Prerequisites: [MATH19X1 or MATH1906 or (a mark of 65 or above in MATH1021 or MATH1001)] and [MATH1902 or (a mark of 65 or above in MATH1002)] Prohibitions: MATH2010 or MATH2033 or MATH2933 or MATH2070 or ECMT3510 Assumed knowledge: MATH19X3 or MATH1907 or a mark of 65 or above in MATH1003 or MATH1023 Assessment: 1 x2-hr exam (70%), 1 x assignment (10%), 1 x quiz (10%); 1 x computational project (10%). To pass the course at least 50% in the final exam is necessary. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Students may enrol in both MATH2970 and MATH3975 in the same semester

The content of this unit of study parallels that of MATH2070, but students enrolled at Advanced level will undertake more advanced problem solving and assessment tasks, and some additional topics may be included.

**STAT2011 Probability and Estimation Theory**

Credit points: 6 Teacher/Coordinator: A/Prof Jennifer Chan Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk Prerequisites: (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2911 Assessment: 2 x quizzes (30%); weekly computer practical reports (5%); a 1-hr computer exam in week 13 (15%); and a final 2-hr exam (50%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to probability, the concept of random variables, special distributions including the Binomial, Hypergeometric, Poisson, Normal, Geometric and Gamma and to statistical estimation. This unit will investigate univariate techniques in data analysis and for the most common statistical distributions that are used to model patterns of variability. You will learn the method of moments and maximum likelihood techniques for fitting statistical distributions to data. The unit will have weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method. By doing this unit you will develop your statistical modeling skills and it will prepare you to learn more complicated statistical models.

Textbooks

An Introduction to Mathematical Statistics and Its Applications (5th edition), Chapters 1-5, Larsen and Marx (2012)

**STAT2911 Probability and Statistical Models (Adv)**

Credit points: 6 Teacher/Coordinator: A/Prof Jennifer Chan Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk Prerequisites: (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and a mark of 65 or greater in (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2011 Assessment: 2 x quizzes (10%); 2 x assignments (5%); computer work (5%); weekly computer lab reports (5%); a computer lab exam (10%) and a final 2-hr exam (70%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2011, with an emphasis on the mathematical techniques used to manipulate random variables and probability models. Common distributions including the Poisson, normal, beta and gamma families as well as the bivariate normal are introduced. Moment generating functions and convolution methods are used to understand the behaviour of sums of random variables. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The notions of conditional expectation and prediction will be covered as will be distributions related to the normal: chi^2, t and F. The unit has weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

Textbooks

Mathematical Statistics and Data Analysis (3rd edition), J A Rice

##### Senior core units of study

**MATH3075 Financial Derivatives**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: 12 credit points chosen from MATH2XXX or STAT2XXX or DATA2X02 Prohibitions: MATH3975 or MATH3015 or MATH3933 Assessment: 2 x assignments (20%); 2-hr final exam (80%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: It is possible to enrol in MATH2070 and MATH3075 in the same semester

This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and heding of exotic options. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Lectures in the mainstream unit are held concurrently with those of the corresponding advanced unit.

**MATH3975 Financial Derivatives (Advanced)**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02) Prohibitions: MATH3933 or MATH3015 or MATH3075 Assessment: 2 x assignments; 2-hr final exam (80%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: MATH2X70 and MATH3975 may be taken in the same semester

This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: the notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and heding of exotic options. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Students enrolled in this unit at advanced level will have to undertake more challenging assessment tasks, but lectures in the advanced level are held concurrently with those of the corresponding mainstream unit.

**STAT3021 Stochastic Processes**

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 1 Classes: 3 lectures per week, tutorial 1hr per week. Prerequisites: STAT2X11 and (MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933) Prohibitions: STAT3911 or STAT3011 Assessment: 2 x Quiz (2 x 15%), 2 x Assignment (2 x 5%), Final Exam (60%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

A stochastic process is a mathematical model of time-dependent random phenomena and is employed in numerous fields of application, including economics, finance, insurance, physics, biology, chemistry and computer science. After setting up basic elements of stochastic processes, such as time, state, increments, stationarity and Markovian property, this unit develops important properties and limit theorems of discrete-time Markov chain and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, such as the memoryless property, super positioning, thinning, Kolmogorov's equations and limiting probabilities. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modeling and analyzing problems of practical interest. By completing this unit, you will develop the essential basis for further studies, such as stochastic calculus, stochastic differential equations, stochastic control and financial mathematics.

**STAT3921 Stochastic Processes (Advanced)**

Credit points: 6 Session: Semester 1 Classes: lecture 3 hrs/week, workshop 1 hr/week Prerequisites: (STAT2011 or STAT2911) and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 Prohibitions: STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT4021 Assessment: 2 x in-class quizzes (30%), 2 x assignments (10%), final exam (60%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

A stochastic process is a mathematical model of time-dependent random phenomena and is employed in numerous fields of application, including economics, finance, insurance, physics, biology, chemistry and computer science. After setting up basic elements of stochastic processes, such as time, state, increments, stationarity and Markovian property, this unit develops basic properties and limit theory of discrete-time Markov chains and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, stopping times and martingales. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modelling and analysing problems of practical interest. By completing this unit, you will develop the essential basis for further studies, such as stochastic calculus, stochastic differential equations, stochastic control and financial mathematics. Students who undertake the advanced unit MATH3921 will be expected to have a deeper, more sophisticated understanding of the theory in the unit and to be able to work with more complicated applications than students who complete the regular MATH3021 unit.

**STAT3022 Applied Linear Models**

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratories per week. Prerequisites: STAT2X11 and (DATA2X02 or STAT2X12) Prohibitions: STAT3912 or STAT3012 or STAT3922 Assessment: 2 x assignment (15%), 3 x quizzes (30%), final exam (55%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such thing as a best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will apply the theory to various real-world problems using statistical software in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

**STAT3922 Applied Linear Models (Advanced)**

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2X11 and [a mark of 65 or greater in (STAT2X12 or DATA2X02)] Prohibitions: STAT3912 or STAT3012 or STAT3022 Assessment: 2 x assignment (10%), 3 x quizzes (35%), final exam (55%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. You will first consider linear models and regression methods with diagnostics for checking appropriateness of models, looking briefly at robust regression methods. Then you will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course you will use the R statistical package to give analyses and graphical displays. This unit is essentially an Advanced version of STAT3012, with additional emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.

##### Senior elective units of study

**STAT3023 Statistical Inference**

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2X11 Prohibitions: STAT3913 or STAT3013 or STAT3923 Assumed knowledge: DATA2X02 or STAT2X12 Assessment: 2 x Quizzes (25%), Computer Lab Report (10%), Computer Exam (10%), Final Exam (55%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such a thing as the best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will apply the methods learnt to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

**STAT3923 Statistical Inference (Advanced)**

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 2 hour advanced workshop. Prerequisites: STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12) Prohibitions: STAT3913 or STAT3013 or STAT3023 Assessment: 2 x Quizzes (20%), weekly homework (5%), Computer Lab Reports (10%), Computer Exam (10%), Final Exam (55%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such thing as a best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will rigorously prove key results and apply these to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

**STAT3888 Statistical Machine Learning**

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2X11 and (DATA2X02 or STAT2X12) Prohibitions: STAT3914 or STAT3014 Assumed knowledge: STAT3012 or STAT3912 or STAT3022 or STAT3922 Assessment: Written exam (40%), major project (50%), computer labs (10%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Data Science is an emerging and inherently interdisciplinary field. A key set of skills in this area fall under the umbrella of Statistical Machine Learning methods. This unit presents the opportunity to bring together the concepts and skills you have learnt from a Statistics or Data Science major, and apply them to a joint project with NUTM3888 where Statistics and Data Science students will form teams with Nutrition students to solve a real world problem using Statistical Machine Learning methods. The unit will cover a wide breadth of cutting edge supervised and unsupervised learning methods will be covered including principal component analysis, multivariate tests, discrimination analysis, Gaussian graphical models, log-linear models, classification trees, k-nearest neighbors, k-means clustering, hierarchical clustering, and logistic regression. In this unit, you will continue to understand and explore disciplinary knowledge, while also meeting and collaborating through project-based learning; identifying and solving problems, analysing data and communicating your findings to a diverse audience. All such skills are highly valued by employers. This unit will foster the ability to work in an interdisciplinary team, and this is essential for both professional and research pathways in the future.

**STAT3914 Applied Statistics Advanced**

*This unit of study is not available in 2020*

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour computer laboratory per week plus an extra hour each week which will alternate between lectures and tutorials. Prerequisites: STAT2912 or (a mark of 65 or above in STAT2012 or DATA2002) Prohibitions: STAT3014 or STAT3907 or STAT3902 or STAT3006 or STAT3002 Assumed knowledge: STAT3012 or STAT3912 or STAT3022 or STAT3922 Assessment: Written exam (40%), major project (50%), computer labs (10%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is an Advanced version of STAT3014. There will be 3 lectures per week in common with STAT3014. The unit will have extra lectures focusing on multivariate distribution theory developing results for the multivariate normal, partial correlation, the Wishart distribution and Hotelling's T^2. There will also be more advanced tutorial and assessment work associated with this unit.

**FMAT3888 Projects in Financial Mathematics**

Credit points: 6 Teacher/Coordinator: Prof Mary Myerscough Session: Semester 2 Classes: 2hr lectures and 3 hrs/workshops per week Prerequisites: (MATH2070 or MATH2970) and (STAT2011 or STAT2911) Assumed knowledge: STAT2X11, MATH2X70 Assessment: Discipline content assignment (10%), discipline content quiz (20%), Discipline project report (10%), discipline project presentation (10%), reflective task (10%), team work process (10%), interdisciplinary project report (20%), interdisciplinary project presentation (10%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Block mode

Mathematics and statistics are powerful tools in finance and more generally in the world at large. To really experience the power of mathematics and statistics at work, students need to identify and explore interdisciplinary links. Engagement with other disciplines also provides essential foundational skills for using mathematical and statistical ideas in financial contexts and in the world beyond. In this unit you will commence by working on a group project in an area of financial mathematics or statistics. From this project you will acquire skills of teamwork, research, wring and project management as well as disciplinary knowledge. You will then have the opportunity to apply your disciplinary knowledge in an interdisciplinary team to identify and solve problems and communicate your findings.

**MATH3971 Convex Analysis and Optimal Control (Adv)**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: Lecture 3hours/week, tutorial 1hr/week Prerequisites: A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02) Prohibitions: MATH4071 Assumed knowledge: MATH2X21 and MATH2X23 and STAT2X11 Assessment: Assignment (15%), assignment (15%), exam (70%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

The questions how to maximise your gain (or to minimise the cost) and how to determine the optimal strategy/policy are fundamental for an engineer, an economist, a doctor designing a cancer therapy, or a government planning some social policies. Many problems in mechanics, physics, neuroscience and biology can be formulated as optimistion problems. Therefore, optimisation theory is an indispensable tool for an applied mathematician. Optimisation theory has many diverse applications and requires a wide range of tools but there are only a few ideas underpinning all this diversity of methods and applications. This course will focus on two of them. We will learn how the concept of convexity and the concept of dynamic programming provide a unified approach to a large number of seemingly unrelated problems. By completing this unit you will learn how to formulate optimisation problems that arise in science, economics and engineering and to use the concepts of convexity and the dynamic programming principle to solve straight forward examples of such problems. You will also learn about important classes of optimisation problems arising in finance, economics, engineering and insurance.

**MATH3076 Mathematical Computing**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr computer lab/wk Prerequisites: 12cp of MATH2XXX or [6cp of MATH2XXX and (6cp of STAT2XXX or DATA2X02)] Prohibitions: MATH3976 or MATH4076 Assessment: One 3 hour exam (55%), 2 assignments (15%+15%), 1 quiz (15%). To pass the course, students much achieve more than 50% on the final exam. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides an introduction to programming and numerical methods. Topics covered include computer arithmetic and computational errors, systems of linear equations, interpolation and approximation, solution of nonlinear equations, quadrature, initial value problems for ordinary differential equations and boundary value problems, and optimisation.

**MATH3976 Mathematical Computing (Advanced)**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr computer lab/wk Prerequisites: A mark of 65 or above in [(12cp of MATH2XXX) or (6cp of MATH2XXX and 6cp of STAT2XXX or DATA2X02)] Prohibitions: MATH3076 or MATH4076 Assumed knowledge: Strong skills in linear algebra and the theory and methods of ordinary and partial differential equations for example (MATH2961 and MATH2965) or (MATH2921 and MATH2922) Assessment: One 3 hour exam (55%), 2 assignments (15%+15%), 1 quiz (15%). To pass the course, students much achieve more than 50% on the final exam. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides an introduction to programming and numerical methods. Topics covered include computer arithmetic and computational errors, systems of linear equations, interpolation and approximation, solution of nonlinear equations, quadrature, initial value problems for ordinary differential equations and boundary value problems, and optimisation.

**MATH3078 PDEs and Waves**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 2 Classes: 3x 1 hour lectures; 1x1 hour laboratory /wk Prerequisites: 12 credit points of MATH2XXX units of study Prohibitions: MATH3978 or MATH4078 Assumed knowledge: [MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22] Assessment: Final exam (70%), 2 assignments (15%+15%). To pass the course, students must achieve at least 50% on the final exam. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

The aim of this unit is to introduce some fundamental concepts of the theory of partial differential equations (PDEs) arising in Physics, Chemistry, Biology and Mathematical Finance. The focus is mainly on linear equations but some important examples of nonlinear equations and related phenomena re introduced as well. After an introductory lecture, we proceed with first-order PDEs and the method of characteristics. Here, we also nonlinear transport equations and shock waves are discussed. Then the theory of the elliptic equations is presented with an emphasis on eigenvalue problems and their application to solve parabolic and hyperbolic initial boundary-value problems. The Maximum principle and Harnack's inequality will be discussed and the theory of Green's functions.

**MATH3978 PDEs and Waves (Advanced)**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 2 Classes: 3x 1 hr lecture; 1x 1 hr laboratory /wk Prerequisites: A mark of 65 or greater in 12 credit points of MATH2XXX units of study Prohibitions: MATH3078 or MATH4078 Assumed knowledge: [MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22] Assessment: Final exam (70%), 2 assignments (15%+15%). To pass the course, students must achieve at least 50% on the final exam. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

The aim of this unit is to introduce some fundamental concepts of the theory of partial differential equations (PDEs) arising in Physics, Chemistry, Biology and Mathematical Finance. The focus is mainly on linear equations but some important examples of nonlinear equations and related phenomena re introduced as well. After an introductory lecture, we proceed with first-order PDEs and the method of characteristics. Here, we also nonlinear transport equations and shock waves are discussed. Then the theory of the elliptic equations is presented with an emphasis on eigenvalue problems and their application to solve parabolic and hyperbolic initial boundary-value problems. The Maximum principle and Harnack's inequality will be discussed and the theory of Green's functions.

**MATH3969 Measure Theory and Fourier Analysis (Adv)**

Credit points: 6 Teacher/Coordinator: Florica Cirstea Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: A mark of 65 or greater in 12 credit points of MATH2XXX units of study Prohibitions: MATH4069 Assumed knowledge: Real analysis and vector spaces. For example MATH2X21 and MATH2X23 Assessment: Assignments (20%), quizzes (20%); 2-hr final exam (60%), Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Measure theory is the study of such fundamental ideas as length, area, volume, arc length and surface area. It is the basis for the integration theory used in advanced mathematics since it was developed by Henri Lebesgue in about 1900. Moreover, it is the basis for modern probability theory. The course starts by setting up measure theory and integration, establishing important results such as Fubini's Theorem and the Dominated Convergence Theorem which allow us to manipulate integrals. This is then applied to Fourier Analysis, and results such as the Inversion Formula and Plancherel's Theorem are derived. The Radon-Nikodyn Theorem provides a representation of measures in terms of a density. Probability theory is then discussed with topics including distributions and conditional expectation.

**MATH3974 Fluid Dynamics (Advanced)**

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: Credit average or greater in 12 credit points of Intermediate Mathematics Prohibitions: MATH4074 Assumed knowledge: [MATH2961 and MATH2965] or [MATH2921 and MATH2922] Assessment: 3 x assignments (30%); final exam (70%). To pass the course at least 50% in the final exam is necessary. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides an introduction to fluid dynamics, starting with a description of the governing equations and the simplifications gained by using stream functions or potentials. It develops elementary theorems and tools, including Bernoulli's equation, the role of vorticity, the vorticity equation, Kelvin's circulation theorem, Helmholtz's theorem, and an introduction to the use of tensors. Topics covered include viscous flows, lubrication theory, boundary layers, potential theory, and complex variable methods for 2-D airfoils. The unit concludes with an introduction to hydrodynamic stability theory and the transition to turbulent flow.

**DATA3404 Data Science Platforms**

Credit points: 6 Teacher/Coordinator: A/Prof Uwe Roehm Session: Semester 1 Classes: lectures, tutorials Prerequisites: DATA2001 OR DATA2901 OR ISYS2120 OR INFO2120 OR INFO2820 Prohibitions: INFO3504 OR INFO3404 Assumed knowledge: This unit of study assumes that students have previous knowledge of database structures and of SQL. The prerequisite material is covered in DATA2001 or ISYS2120. Familiarity with a programming language (e.g. Java or C) is also expected. Assessment: through semester assessment (40%), final exam (60%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides a comprehensive overview of the internal mechanisms data science platforms and of the systems that manage large data collections. These skills are needed for successful performance tuning and to understand the scalability challenges faced by when processing Big Data. This unit builds upon the second' year DATA2001 - 'Data Science - Big Data and Data Diversity' and correspondingly assumes a sound understanding of SQL and data analysis tasks.

The first part of this subject focuses on mechanisms for large-scale data management. It provides a deep understanding of the internal components of a data management platform. Topics include: physical data organization and disk-based index structures, query processing and optimisation, and database tuning.

The second part focuses on the large-scale management of big data in a distributed architecture. Topics include: distributed and replicated databases, information retrieval, data stream processing, and web-scale data processing.

The unit will be of interest to students seeking an introduction to data management tuning, disk-based data structures and algorithms, and information retrieval. It will be valuable to those pursuing such careers as Software Engineers, Data Engineers, Database Administrators, and Big Data Platform specialists.

The first part of this subject focuses on mechanisms for large-scale data management. It provides a deep understanding of the internal components of a data management platform. Topics include: physical data organization and disk-based index structures, query processing and optimisation, and database tuning.

The second part focuses on the large-scale management of big data in a distributed architecture. Topics include: distributed and replicated databases, information retrieval, data stream processing, and web-scale data processing.

The unit will be of interest to students seeking an introduction to data management tuning, disk-based data structures and algorithms, and information retrieval. It will be valuable to those pursuing such careers as Software Engineers, Data Engineers, Database Administrators, and Big Data Platform specialists.